CN105549005A - Dynamic target direction of arrive tracking method based on mesh dividing - Google Patents
Dynamic target direction of arrive tracking method based on mesh dividing Download PDFInfo
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Abstract
The invention discloses a dynamic target direction of arrive tracking method based on mesh dividing. Firstly sensor arrays are arranged in a simulated environment; then a narrow-band signal measurement model of the far-field sensor arrays is established; a source signal model of which space contains noise is constructed; a planar environment is averagely divided into meshes, and the size of the range of the signal incident angle of all the meshes is equal; then a target transfer model is constructed, and the possible state of a target of the next moment is predicted; a Kalman filter equation is generated through combination of the state transfer model of the target and the sensor measurement model, and the signal state value of each divided mesh is solved; and finally the mesh to which the target belongs is determined by utilizing an appropriate method according to the state value of the mesh so that the location of the target can be determined. According to the method, the linear equation of target transfer and signal measurement is constructed by utilizing mesh dividing, and then target tracking is realized through combination of the Kalman filter method so that the disadvantages of the conventional method that computation is complex, computation burden is high and final estimation precision is insufficient can be overcome.
Description
Technical field
The present invention relates to a kind of dynamic object direction of arrival tracking based on stress and strain model, be widely used in the dynamic object real-time follow-up based on wireless senser.
Background technology
Dynamic target tracking utilizes the signal monitoring mobile object transmitting or reflection to be assessed by the movement locus of object of certain algorithm to movement.First need the equipment constantly Received signal strength using specific Received signal strength, and the pre-service such as filtering are carried out to signal, obtain the signal message needed; Then by more specific algorithms, the value that the operation such as filtering or signal conversion directly or indirectly solves needs is carried out to the signal obtained.
At present, target tracking technology is all widely used in civilian and military two fields, is divided into single goal to follow the trail of and the large class of multi-target tracking two in the middle of the research had.No matter which type of is classified, and object is all one, and the target information got is transferred to terminal computer, then carries out various analysis.Single goal is followed the trail of and is mainly contained spatial pursuit and time-space tracking.Current raising is followed the trail of precision and is merged to the data of following the trail of the main direction of studying becoming target tracking.The tracing process of current single goal mainly still carries out the research of simple environment, utilize computing technique and the more efficient information fusion of the communication technology to obtain effective information, and improve measuring accuracy and sensor network life as how less sensor node energy ezpenditure.
Direction of arrival (DirectionOfArrive, DOA) is estimated, as an important research contents in Array Signal Processing, to obtain in recent years and pay close attention to widely, and achieve a series of achievement in research.In the practical implementation in the field such as radar, sonar, due to target signal source normally movement, therefore need to follow the tracks of estimation accurately to the DOA of moving target.The representative algorithm of DOA has MUSIC, ESPRIT etc., but these algorithms are often only used for analyzing the situation worked as target and remain static.If target signal direction is in continuous change, so these algorithms need decomposition repeatedly to receive the covariance matrix of data, are all be not easy to realize from real-time or calculated amount.Tracking based on DOA mainly contains three classes:
1) subspace tracking algorithm
Subspace tracking algorithm is a kind of method of the proper vector corresponding to minimal eigenvalue of ART network array covariance matrix.This kind of algorithm upgrades subspace (signal subspace and noise subspace) information by all means, avoids the continuous repetitive assignment of data covariance matrix or svd, effectively reduces calculated amount.This kind of algorithm has the advantage that calculated amount is little, real-time is good, but its estimated performance in low signal-to-noise ratio situation is not good enough, and itself does not possess decorrelation LMS ability.
2) estimate to replace estimating in real time with segmentation
Traditional DOA estimation method is directly generalized to DOA tracing process by these class methods, by time slice, utilizes the DOA estimated value of per a period of time to replace DOA instantaneous value.This kind of method is simple, and under the condition that target DOA change is less or almost constant, effect is better, and its shortcoming is that real-time and precision are not high, can not process DOA and change occasion faster.
3) filtering class DOA tracking
This kind of effective tracking has a lot.As the EKF (ExtendKalmanFilter of classics, EKF) be use more algorithm, but EKF with only the single order item of the taylor series expansion of nonlinear function, and when system height is non-linear or non-gaussian time, EKF method will cause filtering divergence.Also have Unscented kalman filtering (unscentedKalmanFilter, UKF), particle filter (ParticleFilter, PF) etc.
Summary of the invention
The object of the invention is the deficiency existed for prior art, a kind of dynamic object direction of arrival tracking based on stress and strain model is proposed, the computation complexity the method overcoming traditional DOA tracking technique is high, calculated amount is large, grows computing time to such an extent as to is difficult to meet the problems such as the demand of practical application.Reach calculated amount little, computation complexity is low, can well meet the real-time requirement of practical application.
In order to achieve the above object, design of the present invention is: at plane environment placement sensor array, first set up the narrow band signal measurement model of far field sensor array; Build the source signal model of space Noise; Then average for plane environment grid division, the range size of the signal incident angle of each grid is identical, builds the stress and strain model areal model of array signal; Establishing target metastasis model again, the state that target of prediction lower a moment is possible; The state transition model of last combining target and sensor measurement model production Kalman filter equation, can solve target optimum estimate position.
According to foregoing invention design, the technical solution used in the present invention is:
Based on a dynamic object direction of arrival tracking for stress and strain model, comprise following step:
(1) rectangular coordinate system is set up in monitored area, in the placement sensor of a first-class spacing distance of coordinate axis of coordinate system;
(2) the narrow band signal measurement model of far field sensor array and the source signal model of Noise is built;
(3) monitoring plane environment average grid division G equal portions, the range size of the signal incident angle of each grid is identical, that is, π/G;
(4) the rational metastasis model of establishing target in plane environment, in order to realize Kalman filter tracking, builds Karman equation, so this metastasis model should be linear;
(5) metastasis model of combining target and the measurement model of signal, then according to the principle of Kalman filtering, the dynamic object current location estimated of low complex degree fast.
The narrow band signal measurement model of far field sensor array and the source signal model of Noise is built in described step (2), specific as follows:
The first-class spacing distance of transverse axis that sensor array is listed in rectangular coordinate system is arranged, generally be spaced apart a half-wavelength of signal, i.e. λ/2 (λ is signal wavelength), suppose that the coordinate of first sensor array element is (0,0), then the coordinate of other array element is (λ/2,0), (λ, 0) ..., (N* λ/2,0); The measurement model of sensor is expressed as:
X(t)＝A*S(t)+R(t)(1)
Wherein, t is the moment, the signal that S (t) launches for M the target of t in region, is M*1 dimensional vector; R (t) receives noise for the N number of sensor of t, is N*1 dimensional vector, and A is the steering vector battle array of the N*M dimension of array, and the signal value that X (t) receives for N number of sensor is N*1 vector;
A=[a (θ in above-mentioned
1), a (θ
2) ..., a (θ
m)]
t
Wherein
d in expression formula is sensing station spacing distance, and λ is signal wavelength, θ
irepresent that i-th target arrives the angle of sensor, i=1,2 ..., M, and α (θ
i) represent the guiding vector of N number of sensor to i-th target.
The average grid division of monitoring plane environment in described step (3), it is linear, specific as follows for making to measure equation:
Stress and strain model take initial point as basic point, the upper half area of coordinate axis is on average divided G equal portions, namely the range size of every part is π/G, after grid division, A in formula (1) just becomes the guiding matrix having the N*G of fixing dimension to tie up, can not change according to the target number M in monitored area and change, therefore A be represented by following equation:
A＝[a(θ
1),a(θ
2),...,a(θ
G)]
T
θ wherein
i(i=1,2 ... G) be known when grid division, such as θ
1=π/G, θ
2=2 π/G, θ
g-1=(G-1) π/G, therefore also need to change the S (t) in formula (1) accordingly, S (t) is become the vector of G*1 dimension, but S (t) is sparse, namely in certain grid, target is had, just there is value the position that S (t) is corresponding, other position is all 0.(1) X (t) in formula and R (t) will become G*1 dimensional vector.
Establishing target state probability metastasis model in described step (4), specific as follows:
Hypothetical target moves between three adjacent grids with a kind of probability, i.e. target current grid, the next grid be adjacent, the upper grid be adjacent,
Hypothetical target rests on current grid with the probability of 1/3, or moves to two adjacent grids, then the state mobile equation of target can be expressed as follows:
S(t)＝F*S(t-1)+Q(t)(2)
Wherein S (t-1) represents the value of the signal of previous moment, and F is the transition probability matrix of G*G dimension, the transfer noise that Q (t) is current time t
Wherein f
ijbe the element of F, i, j are the row and column of F respectively.
The position utilizing Kalman filtering to realize dynamic object in described step (5) is estimated in real time, specific as follows:
Build Kalman filter equation
Symbol X (t) in above formula, S (t), S (t-1) are simplified to X respectively
t, S
t, S
t-1.Calculation procedure according to Kalman filtering:
S
t|t-1＝F*S
t-1
P
t|t-1＝F*P
t-1F
T+Q
K＝P
t|t-1*A*(A*P
t|t-1*A
T+R)
-1
P
t＝(E
G*G-K*A)*P
t|t-1
S
t＝S
t|t-1+K*(X
t-A*S
t|t-1)
Wherein K is kalman gain, and F is transition probability matrix, S
tfor the value of current demand signal, S
t-1for the value of previous moment signal, S
t|t-1for the signal estimation value of current time, P
tfor current time S
tcovariance matrix, P
t-1for previous moment S
t-1covariance matrix, P
t|t-1for the covariance matrix of current time prediction signal value, E
g*Gfor the unit matrix of G*G dimension; X
tfor the signal measurements of current time.Q, R are respectively the covariance of Gaussian noise Q (t) and R (t).
Obtain the value of the signal in G grid of current time according to Kalman filtering calculation procedure above, need to calculate the last position of target according to this G element value, have the method that two kinds are feasible:
(1) using the position of mesh coordinate residing for M maximum signal level before in G the element value calculated as M target;
(2) according to the state estimation S of current time t
t, according to clustering algorithm S
tg element be divided into M class, namely suppose monitored area have M target, then ask the mean value of every class all elements mesh coordinate, be used as the position residing for target.
Compared with prior art, the present invention has following apparent advantage:
This method adopts the strategy of stress and strain model, makes signal measurement equation have linear characteristic, advantageously in calculating; And the state of dynamic object moves can be defined between grid and moves, the state at lower a moment of such target just has predictability definitely; Due to the optimal estimation that Kalman filtering is in least mean-square error meaning, in conjunction with linear measurement equation and state transition equation, can optimum estimate be reached, thus improve degree of accuracy; Meanwhile, utilize Kalman filtering can reduce calculated amount and computation complexity greatly, reduce computing time, can actual demand be better met.Can be widely used in based on fields such as DOA dynamic target trackings.
This method constructs linear measurement equation and state transition equation, can perfectly in conjunction with Kalman filtering, improve target locating accurate, most importantly minimizing calculated amount that can be a large amount of and calculation of complex, improve computing velocity, for the target following technology based on direction of arrival is applied to actual laying the first stone.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of this method.
Fig. 2 is coordinate system far-field signal model of the present invention.
Fig. 3 is plane grid division and goal displacement schematic diagram.
Embodiment
In order to understand technical scheme of the present invention better, below in conjunction with accompanying drawing, specific embodiments of the invention are described in further detail.
As shown in Figure 1, based on a dynamic object direction of arrival tracking for stress and strain model, utilize the sensor measurement characteristic after stress and strain model, in conjunction with the linear condition metastasis model built, utilize Kalman filtering algorithm to estimate target current state, be specifically implemented as follows:
(1) set up rectangular coordinate system in monitored area, coordinate system a first-class spacing distance of coordinate axis placement sensor.Build array received signal.Specific as follows:
As shown in Figure 2, signal transacting based on direction of arrival depends on sensor array, rectangular coordinate system is set up needing the scope monitored, even equally spaced placement sensor node on transverse axis, but the spacing distance of sensor node has requirement, be generally λ/2, wherein λ is the wavelength of objective emission signal.Owing to using arrowband far-field signal, the signal of objective emission can be similar to when arriving sensor to be thought parallel, and the value that echo signal arrives different sensors is different, according to Fig. 2, obtains the angle position of target.
τ*c＝(λ/2)sinθθ＝arcsin(2τc/λ)
Wherein τ is the time delay that two sensors receive same signal, and c is the light velocity.θ is signal incident angle
Therefore the angle theta of the line of target and initial point is obtained, i.e. the position of target.
(2) the narrow band signal measurement model of far field sensor array and the source signal model of Noise is built:
As shown in Figure 2, be provided with N number of arrowband far-field signal to arrive on M array element composition aerial array.Suppose there is not mutual lotus root and Sensor gain and phase perturbations between array element, then Received signal strength expression formula can be written as:
In formula, u
it () is Received signal strength amplitude,
be the phase place of Received signal strength, τ is the of short duration time delay of Received signal strength, ω
0it is signal angular frequency.Far field narrow band signal can be write as form below:
So, by formula (2) and (3), following formula can be obtained:
Then total N number of far-field signal of receiving of a kth array element is comprehensively:
In formula, g
kifor a kth array element is to the gain of i-th signal, n
k(t) for a kth array element is at the noise of t, τ
kirelative to the time delay of reference array element when representing that i-th signal arrives kth array element.
In the ideal case, the gain g in formula (5)
kican omit (being normalized to 1), therefore M array element can be arranged in a following matrix at the signal that synchronization receives
Write as vector form:
X(t)＝AS(t)+N
x(t)(7)
If hits is L, then in formula, the M*L n dimensional vector n that X (t) is array, N
xt M*L that () is array ties up noise vector, the N*L n dimensional vector n that S (t) is spacing wave, and A is the space array flow pattern matrix of M*N dimension, and
A＝[a
1(ω
0)a
2(ω
0)...a
N(ω
0)]
It can thus be appreciated that, as long as the expression formula of the delay between array element can be obtained, space array stream shape expression formula matrix just can be write out.
For line array sensor array, if the positional representation of array element is X
k(k=1,2,, M), reference point is positioned at initial point, and the one dimension direction of arrival of incoming signal is θ
i(i=1,2 ..., N), and this angle is the angle of incoming signal and Y-axis, then postpone expression formula and become:
Therefore, formula (7) can be expressed as follows matrix form
(3) average for plane environment grid division G equal portions, the range size of the signal incident angle of each grid is identical.
In planar array, use a kind of measurement of novelty can meet linear expression to make formula (7), because the A in formula (7) changes along with the number of signals change of surveyed area transmitting, this characteristic is unfavorable for calculating, therefore, can as shown in Figure 3, surveyed area is divided G fixing grid, and the range size of each grid is identical.θ in this pattern (10)
i(i=1,2 ..., G) and there is fixing value, θ
1=π/G, θ
2=2 π/G, θ
g-1=(G-1) π/G.Therefore the A in formula (7) is exactly fixing value, A=[a (θ
1), a (θ
2) ..., a (θ
g)]
t.
S (t) again, owing to having divided G grid, S (t) is exactly the vector of G*1 dimension, there is fixing dimension, and in these grids, some grid has target, they transmit, and a little grid does not have echo signal in addition, the grid of echo signal is not had to be 0 in the value of the position of S (t) correspondence.Such as, only have target in the 1st and 2 grids, then S (t) can be expressed as
S(t)＝[s
1(t)s
2(t)0...0]
T
Therefore, S (t) be different with state according to the number of target in grid and change.X (t) and N
xt () is also the same.
(4) metastasis model of establishing target in plane environment.
As shown in Figure 3, in above-mentioned step (3), build Plane Gridding Model, by stress and strain model measuring process linearization.Target shifts in these grids, under certain condition also can the state migration procedure linearization of target at grid.Suppose at detection plane grid division abundant, make a grid can only hold at most a target a moment, namely at synchronization, two target objects can not in same grid.Like this, when multiple target tracking, can not at same grid, result calculate and only have a target because of two targets, thus cause serious error.
Define objective of the present invention can only move at most the distance of a grid in the next moment, and the adjacent grid of its current place grid can only be moved to or rest on its current residing grid, namely the current residing grid of hypothetical target is i-th grid, so there are three possibilities its next position residing for the moment: the i-th-1 grid, i-th grid or the i-th+1 grid.And define objective to move the probability of three grids equal, namely 1/3.Therefore have:
S(t)＝F*S(t-1)+N
s(t)
(11)
In formula, k represents the moment, and S (t) expression transmits, N
st (), for shifting noise, F is the transition matrix of G*G dimension.
Namely
wherein f
ijbe the element of F, i, j are the row and column of F respectively
Formula (11) is required state transition equation, and it has linear characteristic.
(5) metastasis model of combining target and the measurement model of signal, then according to the principle of Kalman filtering, can fast and low complex degree estimate dynamic object current location.
Kalman filtering is an optimization autoregression data processing algorithm, the optimum linear filter of principle that to be least mean-square error be.Carry out the currency of estimated signal according to previous estimated value and a nearest observed data, need state equation and the measurement equation of known system.
According to the analysis of previous step (1) ~ (4), the state equation of dynamic target tracking can be known and measure equation, i.e. formula (7) and formula (11), building Kalman filter equation:
Simplify above formula symbol, use X
trepresent X (t), S
trepresent S (t), S
t-1represent S (t-1).The computation process of Kalman filtering can be as follows:
S
t|t-1＝F*S
t-1
P
t|t-1＝F*P
t-1F
T+Q
K＝P
t|t-1*A*(A*P
t|t-1*A
T+R)
-1
P
t＝(E
G*G-K*A)*P
t|t-1
S
t＝S
t|t-1+K*(X
t-A*S
t|t-1)
Wherein K is kalman gain, and F is transition probability matrix, S
tfor the value of current demand signal, S
t-1for the value of previous moment signal, S
t|t-1for the signal estimation value of current time, P
tfor current time S
tcovariance matrix, P
t-1for previous moment S
t-1covariance matrix, P
t|t-1for the covariance matrix of current time prediction signal value, E
g*Gfor the unit matrix of G*G dimension; X
tfor the signal measurements of current time.Q, R are respectively Gaussian noise N
x(t) and N
sthe covariance of (t).
According to state transition equation and the measured value in each moment, by Kalman filtering, the state estimation of target current time can be known.Therefore, the position determining target according to state estimation is needed.The following two kinds measurement can be had to come the final position of estimating target.
(1) because the Signal estimation value S of current time
tfor the vector of G*1 dimension, according to S
tg element, get the element of M maximal value wherein, the position of this M element, the position of central M target in monitored area.
(2) method is averaging, according to S
tg element, be divided into M class by clustering algorithm, then the mesh coordinate of all elements in each class be averaging, M position coordinates P can be obtained
i.
In formula, i is the sequence number of class, and k is the kth element in class, G
ibe element sets all in the i-th class, g
kfor the coordinate of a kth element grid.
By behind wherein a kind of method is determined above the position of M target, also needing by association algorithm, M value to be associated with in concrete target just can the track of good display-object, and simple conventional association algorithm has KNN association algorithm.Thus realize the track following of dynamic object.
Claims (5)
1., based on a dynamic object direction of arrival tracking for stress and strain model, it is characterized in that, comprise following step:
(1) rectangular coordinate system is set up in monitored area, in the placement sensor of a first-class spacing distance of coordinate axis of coordinate system;
(2) the narrow band signal measurement model of far field sensor array and the source signal model of Noise is built;
(3) monitoring plane environment average grid division G equal portions, the range size of the signal incident angle of each grid is identical, i.e. π/G;
(4) in plane environment, building the rational metastasis model of moving target, in order to realize Kalman filter tracking, building Karman equation, so this metastasis model should be linear;
(5) metastasis model of combining target and the measurement model of signal, then according to the principle of Kalman filtering, fast and the dynamic object current location estimated of low complex degree.
2. the dynamic object direction of arrival tracking based on stress and strain model according to claim 1, it is characterized in that, the narrow band signal measurement model of far field sensor array and the source signal model of Noise is built in described step (2), specific as follows:
The first-class spacing distance of transverse axis that sensor array is listed in rectangular coordinate system is arranged, generally be spaced apart a half-wavelength of signal, i.e. λ/2, wherein λ is signal wavelength, supposes that the coordinate of first sensor array element is (0,0), then the coordinate of other array element be followed successively by (λ/2,0), (λ, 0) ..., (N* λ/2,0), the measurement model of sensor can be expressed as:
X(t)＝A*S(t)+R(t)(1)
Wherein, t is the moment, the value that S (t) transmits for t M target in the zone, is M*1 dimensional vector; The noise that R (t) receives for the N number of sensor of t is N*1 dimensional vector; A is the guiding matrix of the N*M dimension of sensor array, and the signal value that X (t) receives for N number of sensor is N*1 dimensional vector;
A=[a (θ in above-mentioned
1), a (θ
2) ..., a (θ
m)]
t
Wherein
d in expression formula is sensing station spacing distance, and λ is signal wavelength, θ
irepresent that i-th target arrives the angle of sensor, i=1,2 ..., M, and α (θ
i) represent the guiding vector of N number of sensor to i-th target.
3. the dynamic object direction of arrival tracking based on stress and strain model according to claim 1, is characterized in that, the average grid division of monitoring plane environment in described step (3), it is linear, specific as follows for making to measure equation:
Stress and strain model take initial point as basic point, the upper half area of coordinate axis is on average divided G equal portions, namely the angular range size of every part is π/G, after grid division, A in formula (1) just becomes the guiding matrix having the N*G of fixing dimension to tie up, can not change according to the target number M in monitored area and change, therefore A be represented by following equation:
A＝[a(θ
1),a(θ
2),...,a(θ
G)]
T
θ wherein
i(i=1,2 ..., G) and be known when grid division, such as θ
1=π/G, θ
2=2 π/G, θ
g-1=(G-1) π/G, therefore also need to change the S (t) in formula (1) accordingly, S (t) is become the vector of G*1 dimension, but S (t) is sparse, namely in certain grid, target is had, just there is value the position that S (t) is corresponding, other position is all 0, and the X (t) in (1) formula and R (t) will become G*1 dimensional vector.
4. the dynamic object direction of arrival tracking based on stress and strain model according to claim 1, is characterized in that, establishing target state probability metastasis model in described step (4), specific as follows:
Hypothetical target moves between three adjacent grids with a kind of probability, i.e. target current grid, the next grid be adjacent, the upper grid be adjacent,
Hypothetical target rests on current grid with the probability of 1/3, or moves to two adjacent grids, then the state mobile equation of target is expressed as follows:
S(t)＝F*S(t-1)+Q(t)
(2)
Wherein S (t-1) represents the value of the signal of previous moment, and F is the transition probability matrix of G*G dimension, and Q (t) is current time transfer noise,
Wherein, f
ijbe the element of F, i, j are the row and column of F respectively.
5. the dynamic object direction of arrival tracking based on stress and strain model according to claim 1, it is characterized in that, the position utilizing Kalman filtering to realize dynamic object in described step (5) is estimated in real time, specific as follows:
Build Kalman filter equation
Simplify above formula symbol, use X
trepresent X (t), S
trepresent S (t), S
t-1represent S (t-1), the calculation procedure according to Kalman filtering:
S
t|t-1＝F*S
t-1
P
t|t-1＝F*P
t-1F
T+Q
K＝P
t|t-1*A*(A*P
t|t-1*A
T+R)
-1
P
t＝(E
G*G-K*A)*P
t|t-1
S
t＝S
t|t-1+K*(X
t-A*S
t|t-1)
Wherein K is kalman gain, and F is transition probability matrix, S
tfor the value of current demand signal, S
t-1for the value of previous moment signal, S
t|t-1for the signal estimation value of current time, P
tfor current time S
tcovariance matrix, P
t-1for previous moment S
t-1covariance matrix, P
t|t-1for the covariance matrix of current time prediction signal value, E
g*Gfor the unit matrix of G*G dimension; X
tfor the signal measurements of current time, Q, R are respectively the covariance of Gaussian noise Q (t) and R (t);
Obtain the value of the signal in G grid of current time according to Kalman filtering calculation procedure above, then calculate the last position of target according to this G element value, have two kinds of methods:
(1) using the position of mesh coordinate residing for M maximum signal level before in G the element value calculated as M target;
(2) according to the state estimation S of current time t
t, according to clustering algorithm S
tg element be divided into M class, namely suppose monitored area have M target, then ask the mean value of every class all elements mesh coordinate, be used as the position residing for target.
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| CN116299254B (en) * | 2022-09-07 | 2023-10-13 | 无锡国芯微电子***有限公司 | Target tracking method of passive radar finder |
| CN115201799A (en) * | 2022-09-09 | 2022-10-18 | 昆明理工大学 | Time-varying Kalman filtering tracking method for sonar |
| CN116125380A (en) * | 2023-04-19 | 2023-05-16 | 齐鲁工业大学(山东省科学院) | Mobile scene super-resolution positioning method based on Kalman filter |
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